Time Power Law Model

The time power law model is equivalent to the “time hardening” form. Use the time power law model when the value of the material parameter $A$ is very small $(A \leq 10^{- 27})$ . In this case, obtain the equivalent time power law model by defining $q_{0} = {\dot{ε}}_{0}^{\frac{m + 1}{n}} A^{- \frac{1}{n}}$ , keeping the parameters $m$ and $n$ unchanged, and defining ${\overset{\cdot}{ε}}_{0}$ to an arbitrary value greater than zero. Typically, ${\overset{\cdot}{ε}}_{0}$ is set to one. The time power law model rewrites the law in such a way that the typical parameter values do not cause numerical difficulties. In addition, the units of all the parameters are physical, which makes unit conversion easier if required.

The time power law has the following form:

{\dot{\bar{ε}}}^{c r} = {{\dot{ε}}_{0} (\frac{\tilde{q}}{q_{0}})}^{n} ({\dot{ε}}_{0} t)^{m},

where:

${\dot{\bar{ε}}}^{c r}$: is the uniaxial equivalent creep strain rate, $\sqrt{\frac{2}{3} {\dot{ε}}^{c r} : {\dot{ε}}^{c r}},$
$\tilde{q}$: is the von Mises equivalent stress or Hill's anisotropic equivalent deviatoric stress according to whether you defined isotropic or anisotropic creep behavior (see Modeling Simultaneous Creep and Plasticity)
$t$: is the total or the creep time, and
${\overset{\cdot}{ε}}_{0}$ , $m$ , $n$ , and $q_{0}$: are material parameters.